You're in luck: the Airbus A320 flight director has a special mode for exactly this: TRK/FPA (track and flight path angle):

(image source)
When you are on final approach, press the HDG V/S - TRK FPA pushbutton on the FCU. This changes the HDG (heading) selector to TRK (track) and the V/S (vertical speed) selector to FPA (flight path angle). It also changes how the flight director is displayed on the PFD:

Flight Path Director (TRK FPA selected on the FCU)
The display is an alternate way of transmitting flight director commands.
- The Flight Path Vector (FPV) symbol illustrates the track and flight path angle actually being flown.
- The Flight Path Director (FPD) symbol shows the pilot how to intercept and fly the vertical and lateral flight path defined by the FMGC. When the pilot superimposes the FPV and FPD symbols, the aicraft is flying the commanded trajectory.
(Airbus A320 FCOM - Autoflight - Flight Guidance - Flight Director)
Now select the final approach course on the TRK selector on the FCU.
Then select the desired flight path angle (in your case -4.0 for a 4° descent angle) on the FPA selector.
The flight director will now compute how to stay on the track and descent path, taking all head-/tailwind and crosswind components into account. There is no need to manually calculate what vertical speed is required.
You can also engage the autopilot (or keep the autopilot engaged) and it will follow the flight director guidance. If you want to fly manually, just follow the FPD commands on the PFD.
Note that flying in this mode is usually not required for a non-precision approach (except a LOC approach, which should be flown with LOC and FPA modes) because managed modes are recommended when available:
Managed modes are recommended, but selected mode might be useful in case of system or equipment failures.
It is worth recalling that in selected mode, the Flight Path Angle (FPA) easily permits to follow the published descent gradient, but the pilot must still ensure that the vertical trajectory relative to the touchdown point is precisely followed.

(Airbus - Safely Flying Non-Precision Instrument Approaches)
For an aircraft without FPA mode, you can estimate the required vertical speed based on your ground speed (sketch not to scale):

From basic trigonometry, we know that
$$ \tan(\alpha) = \frac{\text{VS}}{\text{GS}} \quad \Leftrightarrow \quad \text{VS} = \tan(\alpha) \text{GS} $$
You probably don't want to use the same units for GS and VS, so with typical units and $\alpha=4^\circ$ we get
$$ \frac{\text{VS}}{\text{ft/min}} = \tan(4^\circ) \frac{\text{kn}}{\text{ft/min}} \frac{\text{GS}}{\text{kn}} \approx 0.070 \times 101 \times \frac{\text{GS}}{\text{kn}} \approx 7.08 \frac{\text{GS}}{\text{kn}} $$